We present a realtime and reliable continuous collision detection (CCD) algorithm between triangulated models that exploits the floating point hardware capability of current CPUs and GPUs. Our formulation is based on Bernstein Sign Classification that takes advantage of the geometry properties of Bernstein basis and Bézier curves to perform Boolean collision queries. We derive tight numerical e...

In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...

it has been shown that, in overdense plasmas of the type encountered in spherical tori, electron Bernstein waves can be excited in a plasma by mode conversion of either an externally launched X mode or an O mode. The electron Bernstein waves are strongly absorbed by electrons in the region where the wave frequency matches the Doppler broadened electron cyclotron resonance frequency or its harmo...

Bernstein algebras were introduced by Holgate [6] as an algebraic formulation of the problem of classifying the stationary evolution operators in genetics (see [8]). Since then, many authors have contributed to the study of these algebras, and there is a fairly extensive bibliography on the subject. Known results include classification theorems for sorre types of Bernstein algebras (for instanc...

An implicit surface is defined as the zero set of a scalar function over 3-space. Sign of implicit function determines whether a point is inside or outside the implicit surface: f (P )  = 0 P is on the surface. < 0 P is inside the surface. > 0 P is outside the surface. An algebraic function is an implicit function where the function is polynomial. By using an A-patch representation of algebra...

In this paper we present a direct method for the numerical solution of the constrained optimal control problem when the gradient information is not available. At this aim, a new control parameterization based on Bernstein basis functions is suggested to convert control problem into nonlinear programing problem (NLP), and then a recently proposed stochastic algorithm called Probabilistic Global ...

Traditional methods for algebraic manipulation of polynomials in Bernstein form try to obtain an explicit formula for each coefficient of the result of a given procedure, such us multiplication, arbitrarily high degree elevation, composition, or differentiation of rational functions. Whereas this strategy often furnishes involved expressions, these operations become trivial in terms of convolut...

Algorithms and identities for (p, q)-Bézier curves via (p, q)-Blossom Abstract In this paper, a new variant of the blossom, the (p, q)-blossom, is introduced, by altering the diagonal property of the standard blossom. This (p, q)-blossom is has been adapted for developing identities and algorithms for (p, q)-Bernstein bases and (p, q)-Bézier curves. We generate several new identities including ...

We elaborate on a correspondence between the coefficients of a multivariate polynomial represented in the Bernstein basis and in a tensor-monomial basis, which leads to homography representations of polynomial functions, that use only integer arithmetic (in contrast to Bernstein basis) and are feasible over unbounded regions. Then, we study an algorithm to split this representation and we obtai...

Collins und Akritas (1976) have described the Descartes method for isolating the real roots of an integer polynomial in one variable. This method recursively subdivides an initial interval until Descartes’ Rule of Signs indicates that all roots have been isolated. The partial converse of Descartes’ Rule by Obreshkoff (1952) in conjunction with the bound of Mahler (1964) and Davenport (1985) lea...